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Solvability of matrix-exponential equations

Abstract:

We consider a continuous analogue of (Babai et al. 1996)’s and (Cai et al. 2000)’s problem of solving multiplicative matrix equations. Given k + 1 square matrices A1, . . . , Ak, C, all of the same dimension, whose entries are real algebraic, we examine the problem of deciding whether there exist non-negative reals t1, . . . , tk such that Yk i=1 exp(Aiti) = C. We show that this problem is undecidable in general, but decidable under the assumption that the matrices A1, . . . , Ak commute. Our...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1145/2933575.2934538

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Institution:
University of Oxford
Department:
Oxford, MPLS, Computer Science
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Computer Science
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Computer Science
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Computer Science
Publisher:
Association for Computing Machinery Publisher's website
Pages:
798-806
Publication date:
2016-07-05
DOI:
URN:
uuid:e363af1b-045a-4d5f-87e6-b4ff24580290
Source identifiers:
619304
Local pid:
pubs:619304
ISBN:
978-1-4503-4391-6

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